1. Field of the Invention
The present invention relates to a method of identifying the dynamic characteristics of a motion mechanism such as an X-Y stage or active anti-vibration apparatus in a semiconductor exposure apparatus in a short period of time with a high precision in the design, manufacturing, and evaluation stages, an exposure apparatus incorporating the method as hardware or software, a system identification apparatus for identifying changes in the characteristics of these apparatuses, a system identification method, and a method of manufacturing devices by using the exposure apparatus.
2. Description of the Related Art
A semiconductor manufacturing apparatus typified by an electron microscope using electron beams, a stepper, a scanner, or the like, incorporates various motion mechanisms such as an X-Y stage, a fine adjustment stage mounted on the X-Y stage, and an anti-vibration apparatus for isolating these stages from floor vibrations. To ensure and to guarantee the performance of the semiconductor manufacturing apparatus, feedback control for the maximum performance of these motion mechanisms must be implemented. In addition, this apparatus must incorporate a control scheme based on a consideration of the relationship in performance between the motion mechanisms, as well as the performance of each motion mechanism as a signal unit.
To produce the maximum positioning performance of the X-Y stage, the anti-vibration and damping characteristics as the performance index of the anti-vibration apparatus must be fully exploited. If such characteristics cannot be fully exploited, and disturbances such as floor vibrations cannot be sufficiently removed, the positioning performance of the X-Y stage cannot be fully produced. Such a phenomenon occurs between the motion mechanisms in the semiconductor exposure apparatus. This problem is important in an apparatus for which high-precision positioning performance is required. In addition, changes in the characteristics of the above motion mechanisms over time must be quickly and quantitatively monitored for the maintenance of the motion mechanisms so as to always keep their performance constant.
Under the circumstances, to form a control system for producing the maximum performance of the motion mechanisms, the characteristics of the motion mechanisms must be quantitatively monitored. The characteristics of the motion mechanisms are defined by viscous damping coefficients, spring constants, resonance frequencies of the mechanisms, and the like. Apparatus design and maintenance can be optimized by quantitatively monitoring these physical parameters and elaborately reflecting the resultant data in control system design. There is no doubt that the characteristics of a control system designed on the basis of optimal and quantitative physical parameters in consideration of the positioning performance required for a movable portion and dynamic conditions such as driving forces to be applied are superior to those of a control system designed without considering such physical parameters.
Modeling of the physical behaviors of motion mechanisms (an X-Y stage, a fine adjustment stage, a anti-vibration mechanism, and the like) as controlled objects is indispensable for the design of a control system. Physical modeling is performed on the basis of the physical laws of dynamics or electromagnetism, and design of an optimal control system allows excellent control on motion mechanisms in a desired state.
A physical model of a small-scale motion mechanism with its actual behavior reflecting therein can be formed relatively easily because the model precisely coincides with the behavior. For a large-scale system formed by combining a plurality of motion mechanisms, parameter approximation, e.g., evaluation of the rigidity of mechanical units and estimation of forces to be generated, is required, and hence an approach using a physical model is not effective in terms of precise control system design.
Even when a control system is designed on the basis of a precise physical model, since a plurality of motion mechanisms aiming at industrial machines is produced, variations in the characteristics of the respective machines must be managed. Even in a plurality of apparatuses based on the same design, the motion mechanisms of the respective apparatuses vary in characteristics owing to slight differences between parts working processes and assembly conditions (e.g., assembly torque). Therefore, design and manufacturing based on the assumption that each apparatus is tuned to an optimal condition are not suited for the mass production of apparatuses.
In addition, the mechanical characteristics (e.g., the frictional resistance and the like of a sliding portion) of a motion mechanism changes over time upon operation of the motion mechanism. This degrades the control performance. When the frictional resistance increases, a positional deviation with respect to a target position remains, resulting in a positioning error. In the worst case, a failure or destruction occurs. For this reason, periodical maintenance is required for the motion mechanism.
The most common method employed in the industrial field to monitor the characteristics of a plurality of motion mechanisms and quantitatively monitor changes in the characteristics of the motion mechanisms over time at the sites of design and production is a method of acquiring frequency characteristic data based on frequency responses. The frequency characteristic data can be acquired by using a measuring device called a frequency response analyzer (popularly called a servo analyzer/FFT (Fast Fourier Transform) analyzer). By using a sine wave sweep method of inputting a sine wave to a controlled object and obtaining a frequency transfer function by changing the frequency in small units, a precise frequency transfer function can be obtained with small increments of frequencies.
A sine wave is input to a target motion mechanism as the amplitude of an input waveform used to vibrate the motion mechanism. The ratio (gain) of this amplitude to the amplitude of a response waveform in a steady state and the phase are measured, and gain and phase characteristics at many measurement points are plotted on a Bode diagram, thereby empirically evaluating the response characteristics and positioning performance of the motion mechanism.
The dynamic characteristics of the motion mechanism are monitored from these characteristics and are reflected in design. By calculating the physical parameters of a plurality of motion mechanisms, the locations of variations are detected. In addition, the performance of a closed loop system provided for a motion mechanism can be grasped by using a gain margin and phase margin which are known in a control theory, and a deterioration in performance is grasped by monitoring the trend of this index over time.
Although measurement data obtained by a frequency response analyzer is useful as data for analyzing the characteristics of a motion mechanism, the measurement data is not used for a control law or maintenance in accordance with a change in the characteristics of the motion mechanism over time. Data conversion into data other than frequency response data is not impossible, but is not executed in practice. That is, the utilization efficiency of this data is poor in spite of the fact that the data is measured by spending a lot of time. This is because empirically obtained frequency transfer functions, and the like, are visible information for evaluating the system, and the frequency transfer function must be rewritten by using a sophisticated technique such as curve fitting so as to write the information as physical models and apply them to control system design. In addition, to obtain parameters for a control system, e.g., a mass, rigidity, viscous damping coefficients, and the like, from the frequency transfer function, this information must be decomposed into discrete data of n-degrees-of-freedom, which are necessary and sufficient for writing the characteristics of an actual motion mechanism as a continuous system (having infinite-degrees-of-freedom).
Assume that the natural frequency of a target motion mechanism is low. In this case, to acquire high-precision frequency characteristics, low-frequency signals of several periods must be input while measurement is performed with small increments of sampling frequencies, thus averaging measurement data. In this manner, appropriate measurement conditions must be set. As the natural frequency of a target motion mechanism is low, the measurement time is prolonged. It should be noted that when the empirical method requiring much measurement time is applied to a plurality of apparatuses in action at the site of production, sine waves are input to the motion mechanisms with a large load. When a measurement method demanding much time is used to grasp variations in characteristics among motion mechanisms of the same type, the method becomes a big factor that decreases productivity. To fully enhance the required measurement performance and perform necessary and sufficient analysis at the sites of design and production, a man-machine interface for an operator, e.g., display of measurement results, data conversion (A/D, D/A), and setting of measurement ranges, is an important factor.
To grasp variations in the characteristics of motion mechanisms with time, diagnosis accompanying measurement must be periodically performed to monitor the trend of obtained measurement results. However, the shutdown of production of ICs by using a semiconductor exposure apparatus must be avoided whenever possible. Therefore, measurement for periodic maintenance and diagnosis needs to be completed in a short period of time. However, measurement using a conventional frequency response analyzer cannot meet the above demand. Under the circumstances, there have been demands for realization of a measurement method of performing measurement in a short period of time with a high analysis precision and an exposure apparatus or anti-vibration apparatus in which the measurement method is implemented as hardware or software.